Examination of Row Dynamics

From the above charts it becomes clear that these spread sheets are characterized by

“Row Dynamics” and “Column Dynamics.” From these dynamics we have calculated four additional points within both the Rows and the Columns of all spreadsheets. These are:

The “Mid-Range.” The mid-range is the mid-point lying between the high and low ratios in the sample, i.e. the average of the highest and lowest numbers in

the set: “(H + L) / 2”.

The “Average” or “Arithmetic Mean.” The sample mean is the sum of all the observations divided by the number of observations.

The “Median.” The median is that number for which half the data is larger than it, and half the data is smaller. It is also called the 50^th percentile. If the data has an odd number of members, the median will be the number in the center of these members; if an even number of members, the median will be the mid-point between the two numbers closest to the center.

The “Median Average.” The Median Average is the mid-point between the Median and the Average (Arithmetic Mean). It is figured as: “(Median + Average) / 2” and is the approximation used throughout this paper – in conjunction with the Midrange – as the best estimate of the dynamics within Rows and Columns.

The High, Midrange, Median Average and Low of Row Dynamics for each Excel spread sheet may now be compared. The following points are made as to this approach.

1) In every Row there exists a Highest Average of the possible averages in the Row.

This Highest Average represents the greatest margin of growth over decline for the time period of that spread for that Row. Conversely the Lowest Average represents the greatest depth of decline over growth for the time period of the spread for that Row.

2) The Midrange between the Highest Average and the Lowest Average is simply the arithmetic division of the distance between these two. It lies half-way between them in any given row. The Midrange represents the arbitrary balance between these two extremes for that Row in any given spread of years. The Midrange is completely independent of, and unconnected to, the Median Average of the Row, other than the fact that they both include the Highest Average and the Lowest Average in their calculus.

3) The Median Average states the accumulated “weight” of all the ratios in the row.

It is unconnected to the Highest Average and the Lowest Average other than it includes both of them as a part of its calculation. It is completely independent of, and unconnected to, the Midrange value and does not take it directly into account in its calculus.

4) When a particular spread of years generates Rows which contain Midrange values and the Median Average values which are quite close to one another, the spread has established a relationship between the most basic ratios of the economy which is balanced and uniform. In the context of our search herein, we use the term “harmonic” to indicate this balance.

5) When a particular spread of years generates Rows which contain Midrange values and Median Average values which are at relatively great distances from one another, the spread has failed to establish a relationship between these basic ratios of the economy. By comparison to the other spreads, the particular spread in question is relatively unbalanced and not uniform.

In the context of our search herein, we use the term “dissonant” to indicate this discord, turbulence or lack of harmony.¹⁸

18 A physical analogy may be helpful to follow the logic at this point. Imagine that a mother and three children are at a playground and that a see-saw is available. A “harmonious” or “balanced” see-saw might be characterized by a simple fulcrum with a board balanced upon it. This would be analogous to the “midrange” (the center of the board) and the “median average” (the weight as distributed on the board) of the spread being very proximate to one another and thereby balanced without further effort or conflict.

The manufacturers of see-saws know, however, that the balance of children and their parents are frequently not evenly distributed. For this reason they place beneath the board a metal set of arches which may be used to adjust the length of the see-saw vis-à-vis the fulcrum in aid of the balance itself. An imbalanced see-saw is characterized by more weight at one end of the see saw than the other. In the analogy under these circumstances the center of the board (midrange of the spread) and the weight imposed upon the board (the median average of the spread) are far apart and a form of imbalance or “dissonance” must result.

A balance may be restored by the addition of weight on one end of the see-saw to bring the balanced weight back, or by the shifting of the board itself from the center point within the metal arches to a point “off -center.” This displacement of the fulcrum beneath the board is equal to the imbalance of weight above the board. In this essay we seek to measure the extent of this displacement as applied systematically to economics.

6) The implication is that when a given spread of years generates Midrange and Median Average values which are proximate to one another and therefore “harmonious” or

“balanced,” some underlying pattern or overriding logic may be at work to create this harmony as opposed to a random and disconnected set of processes and their resulting discordant and dissonant variables.

4.5. “Midrange Minus Median Average”:

An Evaluation of Differing Levels of Dissonance

In order to examine these relationships more carefully and across all spreadsheets, the following program was constructed.

Diagram 1-12, left side, presents the Row Dynamics for the 12-year spread shown in Diagram 1-11. The x-axis indicates the row of the spreadsheet under consideration. The y-axis represents the figure presented by that row as its High, Low, Midrange or Median Average ratio.

Diagram 1-12, right side, presents the graph of the x-axis = Row of the Spread

y-axis = Midrange minus Median Average

When the Median Average is greater than the Midrange, the score is negative; when the Median Average is less than the Midrange, the score is positive. The number along the x-axis again indicates the row of the spread sheet under consideration. The number along the y-axis represents an amount of difference between Midrange and Median Average as found in that row.

The effort to compare systematically the common characteristics of different spreads led us to invent four new terms. Referring to Diagram 1-12 above these are:

“General Dissonance.” The pale blue area running as a ribbon from left to right represents the notion of a “General Dissonance,” i.e. an arbitrary, acceptable distance between Median-Average and Midpoint. When a row possesses a Midrange and a Median Average which are in close proximity to one another, the distance between them will be found within the space designated by pale blue,

“General Dissonance.” After reviewing all spreads of years, this number has been set at +/- 0.05 in as much as it appears applicable to all spreads of years as general field of activity.

“Used General Dissonance.” The amount of dark blue is termed “Used General Dissonance,” i.e. that portion of “General Dissonance” which is actually used by the given row in stating the distance between the Midrange and the Median Average, either as a positive or negative amount surrounding y = 0.

“Acute Dissonance.” The portion in red represents an “Acute Dissonance.” When the distance between Midrange and Median Average falls outside the arbitrarily stated “General Dissonance” the excess is given in red shading. If the distance between the Midrange and the Median Average of a row is great, the “Acute Dissonance” so stated will be signified by large areas of red shading. Lesser amounts of “Acute Dissonance” generate less red shading.

“Claimed Dissonance.” The pink portion running as a ribbon from left to right is “Claimed Dissonance,” i.e. that volume of spread between the high point of “Acute Dissonance” and the low point of “Acute Dissonance.” This is the